Abstract
We consider the infinite-range XY spin glass in the presence of a p-fold anisotropy parameter Dp, favouring p orientations in a plane. This model interpolates between the XY (Dp to 0) and p-state clock (Dp to infinity ) spin glasses. For p>or=4, Dp is irrelevant in what concerns the qualitative behaviour of the Parisi function. Special attention is devoted to the p=3 case, for which the replica-symmetry-breaking scheme leads to very distinct order-parameter functions in the two end-point limits. We analyse the evolution of the Parisi function for varying D3 and find two distinct crossovers in its shape. We evaluate the anisotropy parameter (D3*) at the crossover and find that the Parisi function changes from its conventional behaviour (continuous and monotonically increasing), typical of the XY spin glass (D3 or=D3*).
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